Explain Addition and Subtraction Strategies - 2nd Grade Math

1. What is $46 + 27$ using tens and ones: $(40+6) + (20+7)$?

   $73$. $(40+20)+(6+7)=60+13=73$ by regrouping $13$ as $1$ ten $3$ ones.

2. What property is shown by $7 + 0 = 7$?

   Additive identity property. Adding zero to any number gives the same number.

3. What is the identity property of addition shown by $52 + 0 = 52$?

   Adding $0$ does not change a number. Zero is the additive identity - it doesn't change the sum.

4. What place value fact makes $30 + 4 = 34$ true?

   $30$ is $3$ tens and $4$ is $4$ ones. Each digit represents its place value: tens and ones.

5. What does it mean to decompose $47$ using place value?

   $47 = 40 + 7$. Breaking a number into tens and ones shows its place value parts.

6. What property of operations allows $(8 + 2) + 5 = 8 + (2 + 5)$?

   Associative property of addition. Grouping doesn't change the sum when adding.

7. What property says you can change grouping in addition: $(a+b)+c=a+(b+c)$?

   Associative property of addition. Grouping doesn't change the sum.

8. What property says you can change the order in addition: $a+b=b+a$?

   Commutative property of addition. Order doesn't matter when adding numbers.

9. What is $48 + 19$ using compensation: $48 + 19 = 48 + 20 - 1$?

   $67$. Round 19 up to 20, add to get 68, then subtract 1: $68 - 1 = 67$.

10. What is $61 - 27$ using the idea $61 - 27 = 61 - 20 - 7$?

    $34$. First subtract 20 to get 41, then subtract 7: $41 - 7 = 34$.

11. Which expression shows compensation for $48 + 19$ without changing the sum?

    $48 + 19 = 49 + 18$. Add $1$ to first number, subtract $1$ from second to simplify.

12. What is $29+16$ by adding tens then ones?

    $45$. Add tens: $20+10=30$, then ones: $9+6=15$, total $45$.

13. What is $50 - 26$ using the idea $50 - 26 = 40 - 16$?

    $24$. Regroup: borrow 1 ten from 50, making it $40 + 10 - 26 = 24$.

14. Which equation shows compensation for subtraction: $63-29=(63-30)+1$?

    $63-29=(63-30)+1$. Round $29$ up to $30$, then adjust by adding $1$ back.

15. What is $64+28$ by decomposing $28$ as $20+8$?

    $92$. Add $20$ to get $84$, then add $8$ to get $92$.

16. What is $27 + 35$ by adding tens then ones?

    $62$. Add tens ($20 + 30 = 50$), then add ones ($7 + 5 = 12$), so $50 + 12 = 62$.

17. What is the expanded form of $904$?

    $900 + 0 + 4$. Shows the value of each digit by place: 9 hundreds, 0 tens, 4 ones.

18. What is $52 - 8$ by breaking $8$ into $2 + 6$?

    $44$. First subtract 2 to get 50, then subtract remaining 6: $50 - 6 = 44$.

19. Which expression shows compensation for $62 - 29$ without changing the difference?

    $62 - 29 = 63 - 30$. Add $1$ to both numbers to make subtraction easier.

20. What is $64 - 20$ using place value (subtract tens)?

    $44$. Subtract tens from tens: $60 - 20 = 40$, keep the 4 ones.

21. What is $73-40$ using place value (subtract $4$ tens)?

    $33$. Subtract $4$ tens from $7$ tens to get $3$ tens.

22. What is $81-27$ by subtracting tens then ones?

    $54$. Subtract tens: $80-20=60$, then ones: $1-7$ needs regrouping.

23. What is $73 - 30$ using place value (subtract tens)?

    $43$. Subtract tens from tens: $70 - 30 = 40$, keep the 3 ones.

24. What is the place value of the digit $7$ in the number $478$?

    $70$. The digit 7 is in the tens place, representing 7 tens.

25. What sum is shown by adding tens and ones: $(40 + 7) + (30 + 5)$?

    $70 + 12$. Add tens to tens ($40+30$) and ones to ones ($7+5$).

26. What is $63 - 20$ using place value (subtract tens)?

    $43$. Subtract tens from tens: $60-20=40$, keep $3$ ones.

27. What is the missing number in $38+\Box=45$?

    $7$. Count up from $38$ to $45$: that's $7$.

28. Which equation shows compensation for addition: $49+26=(50+26)-1$?

    $49+26=(50+26)-1$. Round $49$ up to $50$, then adjust by subtracting $1$.

29. What property says $a+0=a$?

    Identity property of addition. Adding zero to any number gives the same number.

30. What is $46+30$ using tens and ones?

    $76$. Add tens: $40+30=70$, then add ones: $6$.

31. What property is shown by $(10 + 6) + 4 = 10 + (6 + 4)$?

    Associative property of addition. Grouping doesn't change the sum when adding three numbers.

32. Find and correct the error: $30 + 9 + 1 = 39$.

    Correct: $30 + 9 + 1 = 40$. The student forgot to add the third number ($1$).

33. What is the place value regrouping shown by $1$ ten being traded for $10$ ones?

    $10 = 10$ ones $= 1$ ten. Ten ones can be regrouped as one ten in place value.

34. What is $54 - 7$ by subtracting to the previous ten first?

    $47$. Subtract to $50$ first: $54-4=50$, then $50-3=47$.

35. What does the digit $7$ represent in the number $472$?

    $70$. The 7 is in the tens place, so it represents 7 tens.

36. What is $72 - 38$ using regrouping with tens and ones?

    $34$. Regroup $7$ tens $2$ ones as $6$ tens $12$ ones to subtract.

37. What is $39 + 8$ by making the next ten?

    $47$. Break $8$ into $1+7$ to make forty: $39+1+7=40+7=47$.

38. What is $62 - 19$ using compensation: $62 - 19 = 62 - 20 + 1$?

    $43$. Round 19 up to 20, subtract to get 42, then add back 1: $42 + 1 = 43$.

39. What is $58 + 7$ by adding ones first?

    $65$. Add ones: $8 + 7 = 15$, which is 1 ten and 5 ones, so $50 + 15 = 65$.

40. What does the digit $3$ represent in the number $538$?

    $30$. The 3 is in the tens place, so it represents 3 tens.

41. What is $46 + 30$ using place value tens and ones?

    $76$. Add tens to tens: $40 + 30 = 70$, keep the 6 ones.

42. What is $39 + 24$ using compensation: $39 + 24 = 40 + 23$?

    $63$. Round 39 up to 40, then subtract 1 from 24 to keep the sum equal.

43. What is $25+35$ using the associative property to add tens first?

    $60$. Group tens: $(20+30)+5=50+10=60$.

44. What is $52-8$ using make-a-ten (subtract $2$ then $6$)?

    $44$. Take $2$ to get $50$, then subtract remaining $6$.

45. Which property is shown by $8 + (2 + 5) = (8 + 2) + 5$?

    Associative property of addition. Grouping doesn't change the sum when adding three numbers.

46. Identify the correct regrouping for $67$ as tens and ones.

    $60+7$. $67$ equals $6$ tens and $7$ ones.

47. What is the expanded form of $356$?

    $300 + 50 + 6$. Shows the value of each digit by place: 3 hundreds, 5 tens, 6 ones.

48. What property of operations allows $6 + 9 = 9 + 6$?

    Commutative property of addition. Numbers can be added in any order with the same result.

49. What property is shown by $34 + 25 = 25 + 34$?

    Commutative property of addition. Numbers can be added in any order; the sum stays the same.

50. Identify the property used to make a ten: $8 + 6 = 8 + 2 + 4$.

    Associative property of addition. Breaks 6 into 2+4 to make 10 with 8, then adds remaining 4.

51. What is $58+7$ using make-a-ten (add $2$ then $5$)?

    $65$. Take $2$ from $7$ to make $60$, then add remaining $5$.

52. What is $58 + 6$ by making a ten first?

    $64$. Break $6$ into $2+4$ to make ten: $58+2+4=60+4=64$.

53. What is the missing number in $\Box-19=30$?

    $49$. Add $19$ to $30$ to find the starting number.

54. What is the relationship between addition and subtraction in $15 - 6 = 9$?

    $9 + 6 = 15$. Addition and subtraction are inverse operations.

55. What is $90-36$ by decomposing $36$ as $30+6$?

    $54$. Subtract $30$ to get $60$, then subtract $6$ to get $54$.

56. What is the correct expanded form of $68$?

    $60 + 8$. Separate the tens place ($60$) from the ones place ($8$).

57. What is the final sum when you combine tens and ones: $70 + 12$?

    $82$. Regroup $12$ ones as $1$ ten and $2$ ones: $70+10+2=82$.

Study these flashcards